Determine the product of the following factors:?

(1-1/2)(1-1/3)(1-1/4)...(1-1/98)(1-1/99)(1-1/100). Those dots ar the elipses there are numbers in between there just too much to write out but follows the same pattern.

2 Answers

Relevance
  • Anonymous
    9 years ago
    Best Answer

    Do the subtraction of the fractions in each term to get

    (1/2) (2/3) (3/4) (4/5) ... (98/99)

    Notice that you can rewrite this product as:

    (1*2*3*4* ... * 98) / (2*3*4* ... * 98*99)

    So most of these terms cancel each other out, leaving you with 1/99.

    If you tried doing this with a calculator, it would not only take you hours, but your answer would probably be wrong with all of the decimal round-off error building up.

    Source(s): BS & MS in mathematics
  • 9 years ago

    .............. n

    Product = Π (1 - 1/k) = 1/n; Lim n→∞ Product → 0

    .............. k=2

Still have questions? Get your answers by asking now.